# Electronvolt

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In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the amount of kinetic energy gained (or lost) by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, BIMP has fixated the definition of the electronvolt equal to 1.602176634×10−19 joules (symbol J), even though the exact measurement of the charge of an electron continues to be improved and as of 2014 is −1.6021766208(98)×10−19  C .

Physics is the natural science that studies matter, its motion and behavior through space and time, and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

## Contents

Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q has an energy E = qV after passing through the potential V; if q is quoted in integer units of the elementary charge and the potential in volts, one gets an energy in eV.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge: positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C2h α / μ0 c0 . It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with the metric prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion (109) electronvolts; it is equivalent to the GeV.

The Planck constant, or Planck's constant, denoted is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second. It is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of ​1299792458 second. According to special relativity, c is the upper limit for the speed at which conventional matter and information can travel. Though this speed is most commonly associated with light, it is also the speed at which all massless particles and field perturbations travel in vacuum, including electromagnetic radiation and gravitational waves. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can approach c, but can never actually reach it. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.

Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors.

MeasurementUnitSI value of unit
EnergyeV1.602176634×10−19 J
MasseV/c21.782662×10−36 kg
MomentumeV/c5.344286×10−28 kg-m/s
TemperatureeV/kB1.160451812×104 K
Timeħ/eV6.582119×10−16 s
Distanceħc/eV1.97327×10−7 m

## Definition

An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 J/C, multiplied by the electron's elementary charge e, 1.602176634×10−19 C. [1] Therefore, one electronvolt is equal to 1.602176634×10−19 J. [2]

The elementary charge, usually denoted by e or sometimes qe, is the electric charge carried by a single proton or, equivalently, the magnitude of the electric charge carried by a single electron, which has charge −1 e. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the elementary positive charge.

The electronvolt, as opposed to the volt, is not an SI unit. The electronvolt (eV) is a unit of energy whereas the volt (V) is the derived SI unit of electric potential. The SI unit for energy is the joule (J).

The International System of Units is the modern form of the metric system and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the second, metre, kilogram, ampere, kelvin, mole, candela, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

## Mass

By mass–energy equivalence, the electronvolt is also a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum (from E = mc2). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1. [3] The mass equivalent of 1 eV/c2 is

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula:

Particle physics is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word particle can refer to various types of very small objects, particle physics usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity.

In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly 1. These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as e and c, unless it is known which units the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined.

${\displaystyle 1\;{\text{eV}}/c^{2}={\frac {(1.602\ 176\ 634\times 10^{-19}\;{\text{C}})\cdot 1\;{\text{V}}}{(2.99\ 792\ 458\times 10^{8}\;{\text{m}}/{\text{s}})^{2}}}=1.782\ 661\ 92\times 10^{-36}\;{\text{kg}}.}$

For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:

1 GeV/c2 = 1.78266192×10−27 kg.

The unified atomic mass unit (u), almost exactly 1 gram divided by the Avogadro number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:

1 u = 931.4941 MeV/c2 = 0.9314941 GeV/c2.

## Momentum

In high-energy physics, the electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., 1 eV). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.

The dimensions of momentum units are LMT−1. The dimensions of energy units are L2MT−2. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (LT−1), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum c.

By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c. [4] [5]

The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS can be achieved by:

${\displaystyle p=1\;{\text{GeV}}/c={\frac {(1\times 10^{9})\cdot (1.602\ 176\ 634\times 10^{-19}\;{\text{C}})\cdot (1\;{\text{V}})}{(2.99\ 792\ 458\times 10^{8}\;{\text{m}}/{\text{s}})}}=5.344\ 286\times 10^{-19}\;{\text{kg}}\cdot {\text{m}}/{\text{s}}.}$

## Distance

In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see mass–energy equivalence). In particular, particle scattering lengths are often presented in units of inverse particle masses.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:

${\displaystyle \hbar ={{h} \over {2\pi }}=1.054\ 571\ 817\ 646\times 10^{-34}\ {\mbox{J s}}=6.582\ 119\ 569\ 509\times 10^{-16}\ {\mbox{eV s}}.}$

The above relations also allow expressing the mean lifetime τ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/τ. For example, the B0 meson has a lifetime of 1.530(9)  picoseconds, mean decay length is = 459.7 μm, or a decay width of (4.302±25)×10−4 eV.

Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy: 1 eV = 8065.544005(49) cm−1.

## Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the Boltzmann constant to convert to the Kelvin scale:

${\displaystyle {1{\text{eV}} \over k_{\text{B}}}={1.602\ 176\ 634\times 10^{-19}{\text{ J/eV}} \over 1.380\ 649\times 10^{-23}{\text{ J/K}}}=11\ 604.518\ 12{\text{ K/eV}}.}$

Where kB is the Boltzmann constant, K is Kelvin, J is Joules, eV is electronvolts.

The kB is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV (kilo-electronvolts), which is equal to 170 MK (million degrees Kelvin).

As an approximation: kBT is about 0.025 eV (≈ 290 K/11604 K/eV) at a temperature of 20 °C.

## Properties

The energy E, frequency v, and wavelength λ of a photon are related by

${\displaystyle E=h\nu ={\frac {hc}{\lambda }}}$${\displaystyle ={\frac {(4.135\ 667\ 516\times 10^{-15}\,{\mbox{eV}}\,{\mbox{s}})(299\ 792\ 458\,{\mbox{m/s}})}{\lambda }}}$

where h is the Planck constant, c is the speed of light. This reduces to

${\displaystyle E{\mbox{(eV)}}=4.135\ 667\ 516\,{\mbox{feVs}}\cdot \nu \ {\mbox{(PHz)}}}$${\displaystyle ={\frac {1\ 239.841\ 93\,{\mbox{eV}}\,{\mbox{nm}}}{\lambda \ {\mbox{(nm)}}}}.}$ [6]

A photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm or frequency 241.8 THz.

## Scattering experiments

In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.

## Energy comparisons

EnergySource
5.25×1032 eVtotal energy released from a 20  kt nuclear fission device
1.22×1028 eVthe Planck energy
10 Y eV (1×1025 eV)the approximate grand unification energy
~624 E eV (6.24×1020 eV)energy consumed by a single 100-watt light bulb in one second (100 W = 100 J/s6.24×1020 eV/s)
300 E eV (3×1020 eV = ~50  J ) [10] the so-called Oh-My-God particle (the most energetic cosmic ray particle ever observed)
2 PeVtwo petaelectronvolts, the most high-energetic neutrino detected by the IceCube neutrino telescope in Antarctica [11]
14 TeVthe designed proton collision energy at the Large Hadron Collider (operated at about half of this energy since 30 March 2010, reached 13 TeV in May 2015)
1 TeVa trillion electronvolts, or 1.602×10−7 J, about the kinetic energy of a flying mosquito [12]
125.1±0.2 GeVthe energy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma [13]
210 MeVthe average energy released in fission of one Pu-239 atom
200 MeVthe average energy released in nuclear fission of one U-235 atom
17.6 MeVthe average energy released in the fusion of deuterium and tritium to form He-4; this is 0.41 PJ per kilogram of product produced
1 MeV (1.602×10−13 J)about twice the rest energy of an electron
13.6 eVthe energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 eV to 10 eV per bond
1.6 eV to 3.4 eVthe photon energy of visible light
1.1 eVthe energy EG required to break a covalent bond in silicon
720 meVthe energy EG required to break a covalent bond in germanium
25 meVthe thermal energy kBT at room temperature; one air molecule has an average kinetic energy 38 meV
230 μeVthe thermal energy kBT of the cosmic microwave background

### Per mole

One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy — this corresponds to the Faraday constant (F96485 C mol−1), where the energy in joules of n moles of particles each with energy E eV is equal to E·F·n.

## Related Research Articles

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle is emitted from an atomic nucleus, transforming the original nuclide to its isobar. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release or Q value must be positive.

In physics, the kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.

Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy of the photon, called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.

The Faraday constant, denoted by the symbol F and sometimes stylized as ℱ, is named after Michael Faraday. In physics and chemistry, this constant represents the magnitude of electric charge per mole of electrons. It has the currently accepted value

The decay energy is the energy released by a radioactive decay. Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide.

Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron–positron pair near a nucleus. For pair production to occur, the incoming energy of the interaction must be above a threshold of at least the total rest mass energy of the two particles, and the situation must conserve both energy and momentum. However, all other conserved quantum numbers of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1.

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In the physical sciences, the wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

The Bohr radius is a physical constant, exactly equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.29177210903(80)×10−11 m.

The hartree, also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. It is defined as 2Rhc, where R is the Rydberg constant, h is the Planck constant and c is the speed of light. Its CODATA recommended value is Eh = 4.3597447222071(85)×10−18 J = 27.211386245988(53) eV.

The word mass has two meanings in special relativity: rest mass or invariant mass is an invariant quantity which is the same for all observers in all reference frames, while relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, the rest mass and relativistic mass are equivalent to the rest energy and total energy of the body, respectively. The term relativistic mass tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity, in favor of using the body's total energy. In contrast, rest mass is usually preferred over rest energy. The measurable inertia and gravitational attraction of a body in a given frame of reference is determined by its relativistic mass, not merely its rest mass. For example, light has zero rest mass but contributes to the inertia of any system containing it.

The Lawson criterion is a figure of merit used in nuclear fusion research. It compares the rate of energy being generated by fusion reactions within the fusion fuel to the rate of energy losses to the environment. When the rate of production is higher than the rate of loss, and enough of that energy is captured by the system, the system is said to be ignited.

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of that particle.

Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged particles that responds collectively to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or charged ion beams, but may also include dust and grains. The behaviour of such particle systems can be studied statistically.

A g-factor is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or nucleus. It is essentially a proportionality constant that relates the observed magnetic moment μ of a particle to its angular momentum quantum number and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton.

The electron rest mass is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about 9.109×10−31 kilograms or about 5.486×10−4 daltons, equivalent to an energy of about 8.187×10−14 joules or about 0.5110 MeV.

Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.

Tests of relativistic energy and momentum are aimed at measuring the relativistic expressions for energy, momentum, and mass. According to special relativity, the properties of particles moving approximately at the speed of light significantly deviate from the predictions of Newtonian mechanics. For instance, the speed of light cannot be reached by massive particles.

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